The following verse spells out a word, letter by letter. "My first" refers to the word's first letter, and so on. What's the word that this verse describes?

My first is in fish but not in snail
My second in rabbit but not in tail
My third in up but not down
My fourth in tiara not in crown
My fifth in tree you plainly see
My whole a food for you and me

Solution:

F R U I T